Application of Green's function method to the study of order-disorder ferroelectrics

Abstract

In this paper, our work which was performed on order-disorder ferroelectrics by the Green's function method is reviewed. First, the Bose Green's function method is modified by introducing three undetermined constants to make the method self-consistent. If the constants are not introduced, the method would give a contradictory result.

Then we apply this method to the transverse Ising model with four-spin coupling to study the properties of phase transitions of order-disorder ferroelectrics. A new condition to determine the transition temperature T_c and the discontinuity at the transition temperature (S ^z)_C has been found. We have also determined the critical values of the model parameters, beyond which the transition is first order. Finally, a comparison of our results with the experimental data of PbHPO₄ and PbDPO₄ indicates that our method is more suitable for describing PbHPO₄-type crystals, and can give a quantitative explanation.